1) The iPod Mini is Windows-formatted from the factory so I believe you should use the iPod Mini CD to format the iPod to Mac-format.
2) No idea about "registering" the iPod Mini.
3) If you're using the same user account on the Mac, both iPods will share the same iTunes library. If you want to each have your own iTunes libraries you will need to create a new user account for the Mac.
4) The smaller drive size of the Mini won't be a problem if you have an iTunes library that is too large to all fit on the Mini. iTunes will automatically create a Smart Playlist containing enough music from iTunes to fill up the iPod Mini.
3G 20GB iPod | Contour Showcase | Shure E5 | Ety ER-4P